This paper collects together various facts about digital waveguide
networks (DWN) used in acoustic modeling, particularly results
pertaining to lossless scattering
at the junction of
digital waveguides. Applications discussed include music synthesis
based on physical models and delay effects
such as artificial
. Connections with Wave Digital Filters
ladder/lattice digital filters
, and other related topics are outlined.
General conditions for losslessness and passivity are specified.
Computational complexity and dynamic range
requirements are addressed.
Both physical and algebraic analyses are utilized. The physical
interpretation leads to many of the desirable properties of DWNs.
Using both physical and algebraic approaches, three new normalized
structures are derived which have only three
multiplications per two-port scattering junction
instead of the four
required in the well known version. A vector scattering
is derived which maximizes generality subject to maintaining desirable
properties. Scattering junctions are generalized to allow any
waveguide to have a complex wave impedance
which is equivalent at
the junction to a lumped load impedance
, thus providing a convenient
bridge between lumped and distributed modeling
involving complex wave impedances yield generalized scattering
coefficients which are frequency dependent and therefore implemented
in practice using digital filters
. Scattering filters
isolable to one per junction in a manner analogous to the multiply in
a one-multiply lattice-filter